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In recent years, the multitask diffusion least mean square (MD-LMS) algorithm has been extensively applied in distributed parameter estimation and target tracking of multitask network. However, its performance degrades under colored input signals or impulsive noises. To overcome these two drawbacks, this paper introduces the subband adaptive filter (SAF) into a multitask network for the first time, and a robust multitask diffusion normalized M-estimate subband adaptive filtering (MD-NMSAF) algorithm is proposed, which solves the global network optimization problem based on the modified Huber (MH) function in a distributed manner, achieves robustness to impulsive noise, and significantly improves the convergence performance of the MD-LMS algorithm. Compared with existing robust multitask diffusion affine projection algorithms (MD-APAs), the computational complexity of the proposed MD-NMSAF algorithm is greatly reduced. In addition, we analyze the mean and mean-square stability conditions of MD-NMSAF, provide theoretical models characterizing the network mean square deviation (MSD) behaviors of transient and steady-state, and further verify their correctness by computer simulations. Simulation results under different network topologies, input signals, filter lengths and impulsive noise types fully demonstrate the performance advantages of the proposed MD-NMSAF algorithm over its competitors in terms of steady-state estimation accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

Recently, the augmented complex-valued normalized subband adaptive filtering (ACNSAF) algorithm has been proposed to process colored non-circular signals. However, its performance will deteriorate severely under impulsive noise interference. To overcome this issue, a robust augmented complex-valued normalized M-estimate subband adaptive filtering (ACNMSAF) algorithm is proposed, which is obtained by modifying the subband constraints of the ACNSAF algorithm using the complex-valued modified Huber (MH) function and is derived based on CR calculus and Lagrange multipliers. In order to improve both the convergence speed and steady-state accuracy of the fixed step size ACNMSAF algorithm, a variable step size (VSS) strategy based on the minimum mean squared deviation (MSD) criterion is devised, which allocates individual adaptive step size to each subband, fully exploiting the structural advantages of SAF and significantly improving the convergence performance of the ACNMSAF algorithm as well as its tracking capability in non-stationary environment. Then, the stability, transient and steady-state MSD performance of the ACNMSAF algorithm in the presence of colored non-circular inputs and impulsive noise are analyzed, and the stability conditions, transient and steady-state MSD formulas are also derived. Computer simulations in impulsive noise environments verify the accuracy of theoretical analysis results and the effectiveness of the proposed algorithms compared to other existing complex-valued adaptive algorithms. [ABSTRACT FROM AUTHOR]

• To overcome the trade-off between fast convergence and low steady-state misalignment under the fixed step-size, we devised a family of variable step-size strategy S-IWF-SSAF algorithms based on the transient model of algorithms by minimizing the mean-square deviation (MSD) on each iteration with some reasonable and frequently adopted assumptions and Price's theorem. • In order to further enhance the tracking capability, an effective reset mechanism is also incorporated into the proposed algorithms. And to guarantee the convergence, the stable step-size range in the mean and mean square sense is concluded. In addition, the computational requirements are exhibited as well. • Monte-Carlo simulations for system identification and adaptive echo cancellation applications certify the proposed algorithms acquire superior performance in contrast to state-of-the-art algorithms within various system inputs under impulsive interference environments. Recently, the sparsity-aware sign subband adaptive filter algorithm with individual-weighting-factors (S-IWF-SSAF) was devised. To accomplish performance enhancement, the variable parameter S-IWF-SSAF (VP-S-IWF-SSAF) algorithm was developed through optimizing the step-size and penalty factor, respectively. Different from the optimization scheme, we devise a family of variable step-size strategy S-IWF-SSAF (VSS-S-IWF-SSAF) algorithms based on the transient model of algorithms via minimizing the mean-square deviation (MSD) on each iteration with some reasonable and frequently adopted assumptions and Price's theorem. And in order to enhance the tracking capability, an effective reset mechanism is also incorporated into the proposed algorithms. It is worth mentioning that the presented algorithms could acquire lower computational requirements and exhibit higher steady-state estimation accuracy obviously and acceptable tracking characteristic in comparison to the VP-S-IWF-SSAF algorithm. In addition, the stable step-size range in the mean and mean square sense and steady-state performance are concluded. And the computational requirements are exhibited as well. Monte-Carlo simulations for system identification and adaptive echo cancellation applications certify the proposed algorithms acquire superior performance in contrast to other related algorithms within various system inputs under impulsive interference environments. [ABSTRACT FROM AUTHOR]

This article proposes an affine-projection-like maximum correntropy (APLMC) algorithm for robust adaptive filtering. The proposed APLMC algorithm is derived by using the objective function based on the maximum correntropy criterion (MCC), which can availably suppress the bad effects of impulsive noise on filter weight updates. But the overall performance of the APLMC algorithm may be decreased when the input signal is polluted by noise. To compensate for the deviation of the APLMC algorithm in the input noise interference environment, the bias compensation (BC) method is introduced. Therefore, the bias-compensated APLMC (BC-APLMC) algorithm is presented. Besides, the convergence of the BC-APLMC algorithm in the mean and the mean square sense is studied, which provides a constraint range for the step-size. Computer simulation results show that the APLMC, and BC-APLMC algorithms are valid in acoustic echo cancellation and system identification applications. It also shows that the proposed algorithms are robust in the presence of input noise and impulse noise. [ABSTRACT FROM AUTHOR]

To improve the robust characteristic and filtering accuracy of the traditional adaptive filtering algorithms (AFAs) under censored regression (CR) model in impulsive interference environments, some robust CR-type AFAs (R-CR-AFAs) have been developed. However, these exiting R-CR-AFAs may suffer from high steady-state misalignment in parameter estimation scenario. Therefore, in this paper, we first construct a unified framework to develop a class of R-CR-AFAs by adopting various robust strategies with error nonlinearities as cost functions. Then the mean and mean-square stability ranges and steady-state convergence behavior of the R-CR-AFAs are analyzed via resorting to some frequently-utilized assumptions and lemmas. In particular, a novel censored regression generalized modified Blake-Zisserman adaptive filtering (CR-GMBZ-AF) algorithm is presented to achieve higher steady-state estimation accuracy contrasted to related R-CR-AFAs benefiting from the advantages of the newly proposed GMBZ criterion based on the unified framework. Numerical simulation experiments manifest that the developed CR-GMBZ-AF algorithm arrives at better learning performance in comparison with state-of-the-art algorithms and the theoretical steady-state model demonstrates good agreement with simulation results under parameter estimation and acoustic echo cancellation scenarios. [ABSTRACT FROM AUTHOR]

In this study, an innovation q-gradient least-mean-square (LMS) spline adaptive filtering (S-AF) algorithm (SAF-qLMS) on the basis of the theory of q-derivative is proposed. The q-calculus confronts the issue of slow convergence by mitigating the over-reliance of LMS-type algorithms on the diffusion of eigenvalues in the input correlation matrix. Compared to conventional derivatives, the SAF-qLMS exploits q-calculus to compute the secant of the cost function, enabling it to take larger steps in the search direction for q > 1. Furthermore, for balancing the convergence rate and steady-state error of SAF-qLMS and solving the deficiency of the fixed step-size, the SAF-VqLMS based on variable step-size is further proposed. Finally, the convergence conditions of the SAF-qLMS are discussed. Simulations in a correlated Gaussian input environment confirm the outstanding performance of the proposed algorithms for nonlinear system identification. [ABSTRACT FROM AUTHOR]

Abstract We propose two sparsity-aware normalized subband adaptive filter (NSAF) algorithms by using the gradient descent method to minimize a combination of the original NSAF cost function and the l 1 -norm penalty function on the filter coefficients. This l 1 -norm penalty exploits the sparsity of a system in the coefficients update formulation, thus improving the performance when identifying sparse systems. Compared with prior work, the proposed algorithms have lower computational complexity with comparable performance. We study and devise statistical models for these sparsity-aware NSAF algorithms in the mean square sense involving their transient and steady-state behaviors. This study relies on the vectorization argument and the paraunitary assumption imposed on the analysis filter banks, and thus does not restrict the input signal to being Gaussian or having another distribution. In addition, we propose to adjust adaptively the intensity parameter of the sparsity attraction term. Finally, simulation results in sparse system identification demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

Abstract A bias-compensated constrained least mean square (BC-CLMS) adaptive filter algorithm for noisy input is proposed. To derive the proposed algorithm, we present a novel cost function whose gradient vector is unbiased. Thereby, the proposed algorithm can mitigate the effect of input noise and obtain an unbiased estimation. Then, the detail performance analysis of the proposed algorithm is also provided. Finally, simulations are carried out to illustrate the advantage of the proposed algorithm. In addition, the correctness of performance analysis is also verified by simulations. [ABSTRACT FROM AUTHOR]

This paper analyzes the statistical behavior of the bias-compensated sign subband adaptive filtering algorithm with individual-weighting-factors (BC-IWF-SSAF) under errors-in-variables (EIV) model. The theoretical expressions for transient and steady-state behaviors of BC-IWF-SSAF in the mean and mean-square senses are derived through utilizing some reasonable assumptions and Price's theorem. Furthermore, the stability ranges of algorithm are provided. To accomplish performance enhancement, the variable step-size version (VSS) of BC-IWF-SSAF, called VSS-BC-IWF-SSAF algorithm, is developed based on the transient model via minimizing the mean-square deviation (MSD) at every iteration to tackle the contradictory requirements of quick convergence rate and high filtering accuracy caused by fixed step-size (FSS). Finally, Monte-Carlo simulations under system identification and acoustic echo cancellation applications certificate the effectiveness of statistical analysis and variable step-size strategy. [ABSTRACT FROM AUTHOR]

In all presented analyses of the normalized subband adaptive filter (NSAF) algorithm, there is a common assumption that the length of the adaptive filter is equal to that of the unknown system. In many practices, however, the adaptive filter usually works in an under-modeling situation. Namely, the length of the adaptive filter is less than that of the unknown system. Therefore, for this case, the existing analysis results for the NSAF algorithm are not applicable. In this paper, we analyze the performance of the deficient length NSAF algorithm based on some reasonable assumptions and approximations. More precisely, the expressions that characterize the transient-state and steady-state mean-square behavior of the algorithm are presented. Simulation results in various scenarios support our theoretical expressions. In addition, based on our analyses, a variable step size NSAF algorithm suitable for the under-modeling case is developed, which improves the performance. [ABSTRACT FROM AUTHOR]

In order to improve the filter׳s performance when identifying sparse system, this paper develops two sparse-aware algorithms by incorporating the l 0 -norm constraint of the weight vector into the conventional normalized subband adaptive filter (NSAF) algorithm. The first algorithm is obtained from the principle of the minimum perturbation; and the second one is based on the gradient descent principle. The resulting algorithms have almost the same convergence and steady-state performance while the latter saves computational complexity. What׳s more, the performance of both algorithms is analyzed by resorting to some assumptions commonly used in the analyses of adaptive algorithms. Simulation results in the context of sparse system identification not only demonstrate the effectiveness of the proposed algorithms, but also verify the theoretical analyses. [ABSTRACT FROM AUTHOR]

The least mean p th power (LMP) and normalized LMP (NLMP) algorithms of adaptive Volterra filter have been successfully developed for nonlinear system identification in α -stable noise environments. However, there exists an inherent tradeoff between the convergence rate and steady-state performance. To address this compromise, a collaborative adaptive Volterra filter based on the convex combination scheme is proposed under the α -stable noise in this paper. By utilizing the convex combination which performs at least as well as the best component filter, the proposed algorithms achieve fast convergence rate and small misadjustment. Furthermore, by following a frame of the generalized combination scheme, two novel combination structures of Volterra filter are presented. Simulations in nonlinear system identification contexts demonstrate that the performances of the proposed algorithms are superior to the existing algorithms under the α -stable noise in terms of the convergence speed and steady state kernel error. [ABSTRACT FROM AUTHOR]

Although the least mean p th power (LMP) and normalized LMP (NLMP) algorithms of adaptive Volterra filters outperform the conventional least mean square (LMS) algorithm in the presence of α -stable noise, they still exhibit slow convergence and high steady-state kernel error in nonlinear system identification. To overcome these limitations, an enhanced recursive least mean p th power algorithm with logarithmic transformation (RLogLMP) is proposed in this paper. The proposed algorithm is adjusted to minimize the new cost function with the p -norm logarithmic transformation of the error signal. The logarithmic transformation, which can diminish the significance of outliers under α -stable noise environment, increases the robustness of the proposed algorithm and reduces the steady-state kernel error. Moreover, the proposed method improves the convergence rate by the enhanced recursive scheme. Finally, simulation results demonstrate that the proposed algorithm is superior to the LMP, NLMP, normalized least mean absolute deviation (NLMAD), recursive least squares (RLS) and nonlinear iteratively reweighted least squares (NIRLS) algorithms in terms of convergence rate and steady-state kernel error. [ABSTRACT FROM AUTHOR]

Abstract: To compensate the linear and nonlinear distortions and to track the characteristic of the time-varying channel in digital communication systems, a novel adaptive decision feedback equalizer (DFE) with the combination of finite impulse response (FIR) filter and functional link neural network (CFFLNNDFE) is introduced in this paper. This convex nonlinear combination results in improving the convergence speed while retaining the lower steady-state error at the cost of a small increasing computational burden. To further improve the performance of the nonlinear equalizer, we derive here a novel simplified modified normalized least mean square (SMNLMS) algorithm. Moreover, the convergence properties of the proposed algorithm are analyzed. Finally, computer simulation results which support analysis are provided to evaluate the performance of the proposed equalizer over the functional link neural network (FLNN), radial basis function (RBF) neural network and linear equalizer with decision feedback (LMSDFE) for time-invariant and time-variant nonlinear channel models in digital communication systems. [Copyright &y& Elsevier]

Abstract: This paper presents a computationally efficient nonlinear adaptive filter by a pipelined functional link artificial decision feedback recurrent neural network (PFLADFRNN) for the design of a nonlinear channel equalizer. It aims to reduce computational burden and improve nonlinear processing capabilities of the functional link artificial recurrent neural network (FLANN). The proposed equalizer consists of several simple small-scale functional link artificial decision feedback recurrent neural network (FLADFRNN) modules with less computational complexity. Since it is a module nesting architecture comprising a number of modules that are interconnected in a chained form, its performance can be further improved. Moreover, the equalizer with a decision feedback recurrent structure overcomes the unstableness thanks to its nature of infinite impulse response structure. Finally, the performance of the PFLADFRNN modules is evaluated by a modified real-time recurrent learning algorithm via extensive simulations for different linear and nonlinear channel models in digital communication systems. The comparisons of multilayer perceptron, FLANN and reduced decision feedback FLANN equalizers have clearly indicated the convergence rate, bit error rate, steady-state error and computational complexity, respectively, for nonlinear channel equalization. [Copyright &y& Elsevier]

Abstract: To overcome the computational complexity of the Volterra filter, a novel adaptive joint process filter using pipelined bilinear polynomial architecture (JPBPF) is proposed in this paper. The proposed architecture consists of two subsections: nonlinear subsection performing a nonlinear mapping from the input space to an intermediate space by the bilinear polynomial filter (BPF), and a linear filter performing a linear mapping from the intermediate space to the output space. The corresponding adaptive algorithms are deduced for the nonlinear subsection and linear filter subsection, respectively. To evaluate the performance of the JPBPF, a series of simulations are presented including nonlinear system identification, predicting of speech signals and nonlinear channel equalization. Compared with the conventional second-order Volterra (SOV) filter and BPF, the JPBPF exhibits a slightly better convergence performance in terms of convergence speed and steady-state error. Moreover, since those modules of a JPBPF can be performed simultaneously in a pipelined parallelism fashion, this would lead to a significant improvement in its total computational efficiency. [Copyright &y& Elsevier]

This paper presents a family of robust set-membership normalized subband adaptive filtering (RSM-NSAF) algorithms for acoustic echo cancellation (AEC). By using a new robust set-membership error bound, the RSM-NSAF algorithm obtains improved robustness against impulsive noises and decreased steady-state misalignment relative to the conventional set-membership NSAF (SM-NSAF) algorithm. To exploit the sparsity of the impulse response, the L0 norm constraint robust set-membership NSAF ( L0 -RSM-NSAF), robust set-membership improved proportionate NSAF (RSM-IPNSAF), and L0 norm constraint robust set-membership improved proportionate NSAF ( L0 -RSM-IPNSAF) algorithms are derived by minimizing a differentiable cost function that utilizes the Riemannian distance between the updated and previous weight vectors as well as the L0 norm of the weighted updated weight vector. Simulations in AEC application confirm the improvements of the proposed algorithms in performance. [ABSTRACT FROM PUBLISHER]

The minimum error entropy (MEE) is an important and highly effective optimization criterion in information theoretic learning (ITL). For regression problems, MEE aims at minimizing the entropy of the prediction error such that the estimated model preserves the information of the data generating system as much as possible. In many real world applications, the MEE estimator can outperform significantly the well-known minimum mean square error (MMSE) estimator and show strong robustness to noises especially when data are contaminated by non-Gaussian (multimodal, heavy tailed, discrete valued, and so on) noises. In this brief, we present some theoretical results on the robustness of MEE. For a one-parameter linear errors-in-variables (EIV) model and under some conditions, we derive a region that contains the MEE solution, which suggests that the MEE estimate can be very close to the true value of the unknown parameter even in presence of arbitrarily large outliers in both input and output variables. Theoretical prediction is verified by an illustrative example. [ABSTRACT FROM PUBLISHER]

As a new addition to the recursive least squares (RLS) family filters, the state space recursive least squares (SSRLS) filter can achieve desirable performance by conquering some limitations of the standard RLS filter. However, when the system is contaminated by some non-Gaussian noises, the performance of SSRLS will get worse. The main reason for this is that the SSRLS is developed under the well-known minimum mean square error (MMSE) criterion, which is not very suitable for non-Gaussian situations. To address this issue, in this paper, we propose a new state space based linear filter, called the state space least p -power (SSLP) filter, which is derived under the least mean p -power error (LMP) criterion instead of the MMSE. With a proper p value, the SSLP can outperform the SSRLS substantially especially in non-Gaussian noises. Two illustrative examples are presented to show the satisfactory results of the new algorithm. [ABSTRACT FROM AUTHOR]

Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adapt then combine MCC and combine then adapt MCC, are developed to deal with the distributed estimation over network in impulsive (long-tailed) noise environments. The cost functions used in distributed estimation are in general based on the mean square error (MSE) criterion, which is desirable when the measurement noise is Gaussian. In non-Gaussian situations, especially for the impulsive-noise case, MCC based methods may achieve much better performance than the MSE methods as they take into account higher order statistics of error distribution. The proposed methods can also outperform the robust diffusion least mean p-power (DLMP) and diffusion minimum error entropy (DMEE) algorithms. The mean and mean square convergence analysis of the new algorithms are also carried out. [ABSTRACT FROM AUTHOR]